something about optical blackhole li li ( 李力 ) dept. phys., fudan univ. [email protected]...
TRANSCRIPT
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Something About Something About Optical Blackhole Optical Blackhole
Li Li (Li Li ( 李力李力 ))Dept. Phys., Fudan Univ.Dept. Phys., Fudan [email protected]@gmail.com
091229 ED 10min presentation091229 ED 10min presentation
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Appl. Phys. Lett. 95, 041106(2009)
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Outline
• Introduction• Begin with Maxwell Equation• Mathematica• Comsol
![Page 4: Something About Optical Blackhole Li Li ( 李力 ) Dept. Phys., Fudan Univ. Aiki.Nogard@gmail.com 091229 ED 10min presentation](https://reader035.vdocument.in/reader035/viewer/2022062422/56649ec65503460f94bd196d/html5/thumbnails/4.jpg)
0
0
E(r,t) E (r)
H(r,t) H (r)i te
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0
E (r)
H (r)ik ns rik re e
e eh h
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0
0 0
2 2 2k s s ns
( )S r ns r
real scalar function of position
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0
1
0
1
D
BE
c t
B
DH
c t
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0
0 0 0
0
0 0 0
0
0
0
0
E
E ik H
H
H ik E
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E(r,t) E (r)
H(r,t) H (r)i te
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E (r)
H (r)ik See
h
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0
0
0
0
1( ln )
1
1( ln )
1
e S e eik
S e h eik
h S h hik
S h e hik
0
0
0
0
e S
S e h
h S
S h e
Short Wave Limit 0k
2 2( )S n
n
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2 2( )S n
n
0
0
0
0
e S
S e h
h S
S h e
SS
n
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S Ss
n S
drn Sds
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d drn n
ds ds
Uniform Medium : n=const.2
20
d r
ds
Straight Line
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0 2 2 2
r
R
dc
n c
( )n n r
Appl. Phys. Lett. 95, 041106(2009).nd const Bigger n!
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Outline
• Introduction• Begin with Maxwell Equation• Mathematica• Comsol
![Page 10: Something About Optical Blackhole Li Li ( 李力 ) Dept. Phys., Fudan Univ. Aiki.Nogard@gmail.com 091229 ED 10min presentation](https://reader035.vdocument.in/reader035/viewer/2022062422/56649ec65503460f94bd196d/html5/thumbnails/10.jpg)
.n const
0 2 2 2
r
R
dc
n c
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11
nr
0 2 2 2
r
R
dc
n c
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0 2 2 2
r
R
dc
n c
11
2nr
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0 2 2 2
r
R
dc
n c
1rn
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1
1.73 ,3
Rn
r
1/ 2
,10
Rn k
r
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Outline
• Introduction• Begin with Maxwell Equation• Mathematica• Comsol
![Page 16: Something About Optical Blackhole Li Li ( 李力 ) Dept. Phys., Fudan Univ. Aiki.Nogard@gmail.com 091229 ED 10min presentation](https://reader035.vdocument.in/reader035/viewer/2022062422/56649ec65503460f94bd196d/html5/thumbnails/16.jpg)
1n
r1n
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•There are solutions of Maxwell equation in short wavelength to describe geometrical optics.
•With designed refractive index(mainly ε), we can control the path of light such as blackhole.
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Prof. Zhifang LinProf. Zhifang LinWeihua WangWeihua WangLianxi ChengLianxi Cheng
林志方 教授林志方 教授王伟华王伟华程恋茜程恋茜
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Derivation of the eikonal equation
21[( ) ( ) ] 0e S S e S e
=02 2( )S n n
0
0
0
0
e S
S e h
h S
S h e
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Differential Equation of Optical Path
drn Sds
d dr
nds ds
2
2
( )
1( )
1[( ) ]
21
2
dS
ds
drS
ds
S Sn
Sn
nnn
d drn n
ds ds
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22
( )sin
( )
r
drr
d
sin .nr const
2 2 2dr rn r c
d c 0 2 2 2
r
R
dc
n c
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d dr dr ns ns r ns
ds ds ds
0s ns
r n
r dnn
r dr
( )n n r
0r dn
rr dr
.r ns const
sin .nr const
.nd const
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1d sK v
ds
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Curvature Vector Unit Normal Line Vector
d drn n
ds ds
dn
nK n sds
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( )dn
K nK K n sds
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1lnK v n
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•Incident wave•Decay range•Symmetry
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1
4
Rn
r 2
Rn
r